Resonance states in the¹²C+¹²C modified Morse potential

Abstract

The resonances in 12 C+ 12 C system described earlier using long range Morse potential determined from resonance data itself, are reexamined in the light of the recent development of the two new methods for identification of resonances in the scattering theory, namely Imaginary Test Potential and Imaginary Phase-shift methods. The high lying resonances are found to be not genuine as pointed out by Kato and Abe, and as such are discarded. This discomfiture is due to the (i) shallow behavior of the Morse potential at the outer edge and (ii) inappropriate insertion of Coulomb tail used in that work. These two deficiencies are now removed in the present study by finding a modified Morse potential with steep rise in the outer edge, and joining smoothly to it a term approximating the Coulomb tail. Calculation of the resonances for this modified Morse potential using the above two methods of identification of resonances in our study, yields more than 25 states with angular momenta 0 + -12 + in the relevant energy regions. This reaffirms the diatomic-like rotational and vibrational picture of the nuclear molecular resonances in 12 C+ 12 C system proposed earlier, and shows close resemblance with the physics of diatomic molecules, a phenomenon belonging to altogether a different area. It is revealing that the similarity extends right upto the level of potential which is Morse type in both the cases. This study also reveals new features of heavy ion potential.

Resonant states and pseudospin symmetry in the Dirac-Morse potential

“…Nasser et al [38] have adopted the J-matrix method to examine not only the bound states but also resonances associated with the rotating Morse potential model. Satpathy et al [39][40][41][42] have employed the long-ranged Morse potential between two carbon nuclei in order to obtain many vibrational states which can be compared with observed resonance levels. Kato and Abe [43] have applied the Morse potential model to the 12 C-12 C system as a typical example of the molecular resonances observed in many lighter heavy-ion collisions.…”

Resonance states in 16O+16O, 12C+16O, α+16O and α+12C with modified Morse potentials

“…However, they could not reproduce the high-lying ones. There upon we identified [18] the two discomfitures of our potential: (i) its shallow behavior at the outer edge, which to be realistic should be steeply rising like the Wood-Saxon potential and (ii) the inappropriate insertion of Coulomb potential in the tail region violating the continuity. To repair these two defects we constructed a potential retaining all its essential features like depth, range and the repulsive soft core, with the incorporation of the above two features, and termed it as modified Morse potential [18] given by…”